I see this as a false dichotomy - the real most correct way is less expensive, it's just that quite often people who think they're aiming at perfection are instead actually experimenting with different approaches at random with no clear benefit.

You don't need to cut corners to achieve cost effectiveness and tech debt is just that - debt, which always has to be paid eventually - either through expensive bugfixing, a rewrite or bad user experience.

The project's I've been in that went over budget usually had one or more of the following:

-Too large of a scope vs budget.

-Bad or no architecture whatsoever.

-Increasing personnel instead of reducing scope.

On the other hand projects with an architecture, a set of clear conventions and flexible scope fared much better.